Macroscopic fundamental diagram in simple street networks

Macroscopic fundamental diagrams (MFDs) on simple street networks are studied analytically and numerically. We consider nonlinear circuit model that consists of road elements with piecewise linear fundamental diagram. We find that MFDs of the model are discontinuous and sawtooth like. Meanwhile, simulations of optimal velocity model on the same street networks yield continuous MFDs, that are observed in real urban traffic.